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Weerstandskracht $$F_d = C_d · 1/2 ρ_f v^2 A_\⟘$$
$$v_t = √{{4 (ρ_v - ρ_f) g D }/{3 C_d ρ_f}}$$
Warmtebalans $${dq}/{dt} ={d(ρc_pVT)}/{dt} = ρc_pV{dT}/{dt} = Φ_{q, in} - Φ_{q, uit} + P_q$$
Transportvergelijkingen $$φ_{q,x} = -λ {dT}/{dx}$$
$$φ_{m,x} = -D {dC}/{dx}$$
$$φ_{p_z,x} = -µ {dv_z}/{dx}$$
$$Φ = A·φ$$
Warmtetransport $$Φ_q = A·U·ΔT$$
$$U = 1/{∑↙i{1/h_i}+∑↙j{D_j/λ_j}$$
Instationair warmtetransport $$x_i = √{πat}$$
$${Fo} = {at}/d^2$$
$$M = {T – T_1}/{T_0 – T_1}$$
Convectie van warmte $$Φ_q = hAΔT$$
$$Nu = {hd}/λ$$
$$Re = {ρvd}/µ$$
$$Pr = {c_pµ}/λ$$
$$⟨Nu⟩_{plaat} = 2·Nu_x = 0,664 · Re^{1/2} · Pr^{1/3}$$
$$Gr = {d^3gρ^2}/{µ^2}·{Δρ}/⟨ρ⟩$$
$$⟨Nu⟩_{bol, vrij} = 2,0$$
$$⟨Nu⟩_{platen, vrij, stabiel} = 1,0$$
Warmtewisselaars $${dq}/{dt} = (φ_mc_p)_1(T_{1A} - T_{1B}) + (φ_mc_p)_2(T_{2B} - T_{2A}) = 0$$
$$ΔT_{lm} ={ΔT_A-ΔT_B}/{ln({ΔT_A}/{ΔT_B})}$$
$$φ_q = UA·ΔT_{lm}$$
Grensvlak $$p = H·x$$
$$m = 10^{-5}·H·(M_W/M_L)·(ρ_L/ρ_W) = 2,19·10^{-11}·p/T·H$$
Massatransport (diffusie en convectie) $$Φ_m = A·k·(C_1-C_2) = A k ΔC$$
Massabalans $${dm}/{dt} = Φ_{m, in} - Φ_{m, uit} + P_m$$
$$τ=V/Φ_v$$
Instationair stoftransport $$x_i = √{πDt}$$
$${Fo} = {Dt}/d^2$$
$$M = {C – C_1}/{C_0 – C_1}$$
Convectie van massa $$Sh = {kd}/D$$
$$Sc = {µ}/{ρD}$$
Numerieke methoden $$C_d = {24}/{Re} + {3,6}/{Re^{0,313}}+{0,42}/{1+42500Re^{-1,16}}$$
$$ΔT = {λ/{ρc_p}} · {T_{i-1}-2T_i+T_{i+1}}/{Δx}^2Δt$$
$${λ}/{ρc_p}Δt < 1/2{Δx}^2$$
Mechanische-energiebalans $${dE_m}/{dt} = Φ_m(1/2(v_1^2-v_2^2) + g(z_1-z_2) + {p_1-p_2}/ρ) + Φ_w - Φ_f$$
De wet van Bernoulli $$1/2(v_1^2-v_2^2) + g(z_1-z_2) + {p_1-p_2}/ρ =0$$
$$A_{vc}/A_o = 0,62$$
Windenergie $$P_{th} = {16}/{27}·1/2·ρ·v_1^3A$$
$$P = 1/2 C_pρv_w^3A$$
$$C = {E_{jaar}}/{P_{max}t_{jaar}}$$
Leidingsystemen: de frictiefactor $$Δp = 4f·1/2 ρ v^2L/D$$
Leidingsystemen: het weerstandsgetal $$e_{f, totaal} = ∑↙i{(4f1/2v^2L/D)_i} + ∑↙j{(K_w 1/2v^2)_j}$$
Macroscopische impulsbalans $${dp_x}/{dt} = Φ_{p,x,in} - Φ_{p,x,uit} + F_x$$
Impulstransport $$τ_{zx} = -µ {dv_x}/{dz}$$
Microscopische impulsbalans $$ρ ( {∂v_x/∂t} + v_x{∂v_x/∂x} + v_y{∂v_x/∂y} + v_z{∂v_x/∂z} ) = - ( ∂τ_{xx}/∂x + ∂τ_{yx}/∂y + ∂τ_{zx}/∂z ) - ∂p/∂x + ρg_x$$
Niet-newtonse vloeistoffen $$τ_{zx}=-K({dv_x}/{dz})^n$$